Frequency tuning based on pressure control is demonstrated on an etalon-narrowed Littrow-type single-mode dye laser oscillator pumped by a copper vapor laser. The oscillator is installed in a pressure vessel and the frequency is scanned by controlling the refractive index of the air inside the vessel. To scan the dye laser frequency continuously without mode hopping, the cavity length is also controlled in addition to the pressure change. The frequency stability of the oscillator in a pressure vessel is within 100 MHz/1.5 hr and the oscillator can be scanned with a frequency range of 29 GHz at a scan rate of around 2.5 GHz/min.